On the Geno-GPITT framework

Abstract

The decades of research by Professor R. M. Santilli saw the advent of iso-, isodual-, geno-, genoisodual-and hyper-mathematics and corresponding lifting of mechanics and quantum mechanics [see for example: 1, 2]. This then removed a multitude of inadequacies existing in various branches of science e.g. general and special relativity, quantum mechanics, quantum chemistry, astrophysics, cosmology, particle physics, nuclear physics, and so on. Thus we can safely say that the new mathematics of Santilli produced new sciences for a new era. However, on these lines a rigorous investigations in the field of thermodynamics in general and nonequilibrium thermodynamics in particular have not been carried out so far. Of course, the the recent attempts of Dunning-Davies [3] have produced iso-thermodynamics, isodual-thermodynamics and geno-thermodynamics. However, before the present author's attempt [4] no efforts have been made to develop geno-nonequilibrium thermodynamics. Therefore, as a representative example we have developed Geno-GPITT based on the direct use of the second law of thermodynamics, genotopically lifting the mathematical statements of zeroth, first and second laws of thermodynamics [4], taking care of Bridgman's description of the universe of operations of thermodynamics [5, 6] and at the same time without incorporating the local equilibrium assumption that classical irreversible thermodynamics uses [7]. In the first step to develop Geno-GPITT we arrive directly from the genotopically lifted Clausius' inequality the genoentropy function. Next our investigation surfaces out four geno-nonequilibrium thermodynamics time's arrows and in the respective geno-nonequilibrium thermodynamics spaces the second law of thermodynamics is followed flawlessly. The Geno-De Donderian equation and the Geno-Gibbs relation have been derived. The genoentropy balance equation reveals a new term in the expression of genoentropy source strength that accompanies dilatation process and originates if heat and/or momentum fluxes exit. This mechanism is in addition to that contributes to the bulk viscosity via viscous pressure. We have also described the status of universal inaccessibility principle [8, 9] vis-á-vis genomathematics. The conclusion is that they complement one another. Also we have commented on the development of geno-nonequilibrium thermodynamics of complex and antimatter systems.